Problem: Ishaan is 2 times as old as Emily. 30 years ago, Ishaan was 7 times as old as Emily. How old is Ishaan now?
Answer: We can use the given information to write down two equations that describe the ages of Ishaan and Emily. Let Ishaan's current age be $i$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $i = 2e$ 30 years ago, Ishaan was $i - 30$ years old, and Emily was $e - 30$ years old. The information in the second sentence can be expressed in the following equation: $i - 30 = 7(e - 30)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to solve our first equation for $e$ and substitute it into our second equation. Solving our first equation for $e$ , we get: $e = i / 2$ . Substituting this into our second equation, we get: $i - 30 = 7($ $(i / 2)$ $- 30)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $i - 30 = \dfrac{7}{2} i - 210$ Solving for $i$ , we get: $\dfrac{5}{2} i = 180$ $i = \dfrac{2}{5} \cdot 180 = 72$.